If the earth did not rotate but still orbited the sun, how often you would get to see a full moon?
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$\begingroup$ Once a (Lunar) month. $\endgroup$– AlexanderSep 17, 2020 at 18:20
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$\begingroup$ @sphennings. To our mutual disappointment, it does not. $\endgroup$– TwelvfthSep 17, 2020 at 18:48
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$\begingroup$ @Alexander. But if the phase of the moon is consequence of earth's shadow on the moon and the earth isn't rotating then doesn't that mean it's possible for an earthling-on-the-surface to never witness a full moon? Therefore, the answer is not as simple as you suggest, i.e., once a lunar month. $\endgroup$– TwelvfthSep 17, 2020 at 18:50
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4$\begingroup$ @Twelvfth The phase of the moon does not depend on the earth's shadow. Lunar eclipses are the only times when the earth's shadow impacts the phase of the moon. The rest of the time it depends on whether you're seeing the bright half or the dark half of the moon. I suggest looking up how moon phases work. $\endgroup$– ThisIsAQuestionSep 17, 2020 at 18:55
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It depends on what you mean by non-rotating.
There are two ways your planet could be non-rotating. Either a certain point on the planet is always facing the same direction relative to the sun, or the planet goes through one day/night cycle per year. The first option is known as tidal locking, and the second is known as not rotating in the sidereal frame.
Tidal Locking
How often you see a full moon will depend on where on the planet you are. Full moons happen when the moon is on the opposite side of the planet from the sun. This will happen once per orbit of the moon (lunar month), and how the planet is rotating does not impact this. What will change is how often you get to see the full moon.
If you're on the "day" side of the planet, you will never see the full moon. When it happens, the moon will be on the wrong side of the planet for you to see it. If you're on the "night" side of the planet, you will always see the full moon, so you'll get one full moon per lunar month.
Not Rotating in the Sidereal Frame
Again, whether you get a full moon will depend on where on the planet you are during the full moon. However, unlike with tidal locking, this location will be different each time a full moon happens. As a rough estimate, you will see the full moon when it's night, and you won't when it's day. This means half the year you will see the full moon once per lunar month, and the other half you will never see the full moon. Of course only a few of those full moons will have it in the middle of the sky. For the rest the full moon will be closer to the horizon.
